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ACT Math : Algebra

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Example Questions

Example Question #171 : Exponents

What is the sum of the solutions of the equation x²-2x-8=0?

Possible Answers:

-6

-10

-2

Correct answer:

Explanation:

The equation factors to (x-4)(x+2)=0, indicating that the roots are x=-2,4. The sum of these two roots is 2.

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Example Question #1 : How To Use Scientific Notation

What is the number 350,000,000 in scientific notation?

Possible Answers:

3.5 x 10⁵

3.5 x 10⁶

3.5 x 10⁹

3.5 x 10⁷

3.5 x 10⁸

Correct answer:

3.5 x 10⁸

Explanation:

350,000,000 = 3.5 x 10⁸(exponent is equal to the number of decimal points shifted)

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Example Question #872 : Algebra

Given the equation 2xy + 4x² - y = 2x, if x = 2, what does y equal?

Possible Answers:

-4

Correct answer:

-4

Explanation:

We plug in the value given for x and solve for y.

2xy + 4x² - y = 2x

2(2)y + 4(2)² - y = 2(2)

4y + 4(4) - y = 4

4y - y + 16 = 4

3y = -12

y = -4

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Example Question #2 : How To Use Scientific Notation

How do you express 657,800 in scientific notation?

Possible Answers:

6.578 × 10⁴

65.78 × 10⁶

6.578 × 10³

65.78 × 10⁴

65.78 × 10³

Correct answer:

65.78 × 10⁴

Explanation:

657800 = 6.578 × 10⁵

657800 = 65.78 × 10⁴

Exponent on 10 is the number of decimal points over the number has shifted.

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Example Question #5 : Other Exponents

2 × 10⁰ + 3 × 10² + 4 × 10⁴ = ?

Possible Answers:

40,320

400,032

40,302

4,032

432

Correct answer:

40,302

Explanation:

2 × 10⁰ + 3 × 10² + 4 × 10⁴ =

2 + 300 + 40,000 = 40,302

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Example Question #871 : Algebra

Give this number in scientific notation:

125,000,000

Possible Answers:

$12.5\times 10^{10}$

$1.25\times 10^{8}$

$1.25\times 10^{9}$

$1.25\times 10^{7}$

$12.5\times 10^{8}$

Correct answer:

$1.25\times 10^{8}$

Explanation:

There are six zeros and two more number places, for a total of eight, so 125,000,000 is equivalent to $1.25 \times 10^{8}$ .

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Example Question #872 : Algebra

Simplify the following expression:

$(4(i^{2}-3))^{\frac{1}{2}}$

Possible Answers:

Correct answer:

Explanation:

$(4(i^{2}-3))^{\frac{1}{2}} =(4(-1-3))^{\frac{1}{2}} =(4(-4))^{\frac{1}{2}}$

$=(-16))^{\frac{1}{2}}=\sqrt{-16}=\sqrt{(16)(-1)}=4i$

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Example Question #873 : Algebra

What is the number $\dpi{100} \small 256,000,000,000$ in scientific notation?

Possible Answers:

$\dpi{100} \small 2.56\times 10^{10}$

$\dpi{100} \small 2.56\times 10^{11}$

$\dpi{100} \small 2.56\times 10^{13}$

$\dpi{100} \small 2.56\times 10^{9}$

$\dpi{100} \small 2.56\times 10^{12}$

Correct answer:

$\dpi{100} \small 2.56\times 10^{11}$

Explanation:

$\dpi{100} \small 256,000,000,000 = 2.56\times 10^{11}$

The exponent is equal to the number of decimal points shifted.

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Example Question #5 : How To Use Scientific Notation

Convert from scientific to decimal notation:

$2.3\times 10^{4}$

Possible Answers:

0.0023

230,000

23,000

2300

0.00023

Correct answer:

23,000

Explanation:

In this case the exponent is positive hence you have to move the decimal point 4 places to the right from where it is in the problem giving us

23,000

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Example Question #874 : Algebra

Convert from decimal to scientific notation:

0.0000034

Possible Answers:

$3.4\times 10^{-5}$

$3.4\times 10^{-4}$

$3.4\times 10^{-6}$

$3.4\times 10^{6}$

$3.4\times 10^{7}$

Correct answer:

$3.4\times 10^{-6}$

Explanation:

In this case you have to move the decimal point 6 places to the right. When you move the decimal point to the right the exponent becomes negative. Similarly when you move the decimal point to the left the exponent is positive. Also, to the left of the decimal place there can be only one digit.

$3.4* 10^{-6}$

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ACT Math : Algebra

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #171 : Exponents

Example Question #1 : How To Use Scientific Notation

Example Question #872 : Algebra

Example Question #2 : How To Use Scientific Notation

Example Question #5 : Other Exponents

Example Question #871 : Algebra

Example Question #872 : Algebra

Example Question #873 : Algebra

Example Question #5 : How To Use Scientific Notation

Example Question #874 : Algebra

All ACT Math Resources

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